Ta có $\cos^2\alpha=\cos^2(180^o-\alpha)$, $\cos^2\alpha=\sin^2(90^o-\alpha)$
$\cos^210^o+\cos^220^o+\cos^230^o+...+\cos^2170^o+\cos^2180^o$
$=2\cos^210^o+2\cos^20^o+...+2\cos^280^o+\cos^290^o+\cos^2180^o$
$=2(\cos^10^o+\cos^80^o)+2(\cos^220^o+\cos^270^o)+2(\cos^230^o+\cos^260^o) +2(\cos^240^o+\cos^250^o) +\cos^290^o+\cos^180^o$
$=2.1+2.1+2.1+2.1+1+0$
$=9$